As a first example, we consider a perfectly electrically conducting (PEC) rectangular plate of dimension \(\ell \times \ell /2\)  (\(\ell =15\,\) ). Because of the structure's simplicity, it is straightforward to analyze using most full-wave solvers. Characteristic modes are calculated via (REF ) using matrices \(\tilde{{S}}\)  obtained from each method. Modal significances \(|t_n|\)  and characteristic anglesFor modes with low modal significance \(|t_n|\ll 1\) , the characteristic angle \(\alpha _n\)  calculated by (REF ) is highly sensitive to small numerical errors, leading to jumps. These errors can largely be avoided by a slight reformulation \(\alpha _n = \arg (1+2 t_n)/2 + \pi /2 \in [\pi /2,3\pi /2]\)  and excluding modes with \(|t_n|\le \epsilon \) , where the parameter \(\epsilon \)  effectively sets the maximum detectable eigenvalue magnitude \(|\lambda _n| \le \epsilon ^{-1}\)  in the system matrix formulation (REF ). [1]}
\(\alpha _n = \arg (t_n)\,\in \,\left[\pi /2,3\pi /2\right]\) 
